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From what I understand, electromagnetic radiation produced by an antenna is of the frequency that corresponds to the motion of the electrons moving around in the antenna. And I assume that the electrons in most set ups are generally vibrating in an approximately sinusoidal motion. But sinusoidal is definitely not the only periodic shape we can get electrons to vibrate in. We can have square waves or saw-tooth waves.

My question is is there any detectable difference or any additional theoretical property individual photons have that are produced or carry some other non-sinusoidal wave shape, or are photons' energy states fully described by their frequency?

To be clear I'm interested in the resulting properties of individual quanta and not statistical group properties.

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    $\begingroup$ A multi-frequency broadcast (i.e. anything but a pure sine wave) will be made up of multiple photons. $\endgroup$
    – Jon Custer
    Jun 29, 2016 at 19:42
  • $\begingroup$ Sunlight is pretty "irregular", if you want. It contains a wide range of frequencies and if you want to express that with quanta, you can do so using an ensemble. An individual quantum, OTOH, is just a single measurement on the field, so it can't tell you very much about the ensemble. That's no different from the classical case, where a single wave sample can't tell you much about the entire wave, either. $\endgroup$
    – CuriousOne
    Jun 29, 2016 at 19:50
  • $\begingroup$ Remember that a square or saw-tooth wave is simply a combination of several sinusoidal waves at certain frequencies and amplitudes. When you get down to it, a (co)sine wave is really the only fundamental periodic shape you can have. $\endgroup$
    – Jim
    Jun 29, 2016 at 20:01
  • $\begingroup$ @Jim I understand that mathematically we can decompose (almost) any complex wave into an infinite Fourier series. But that fact alone doesn't necessarily imply that every physical electromagnetic wave isn't just approximated by but exactly equal to a finite combination of perfect (co)sine waves. $\endgroup$ Jun 29, 2016 at 20:07
  • $\begingroup$ @JonCuster If that is true, would you mind expanding that into an actual answer with perhaps examples or sources? $\endgroup$ Jun 29, 2016 at 20:08

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Although you might drive your antenna (and the internal electrons) with a sawtooth wave, the resulting antenna emission is decomposed into "modes" of the antenna, which depend on the length, shape etc. The Mode will correspond to photons (well, in antennas you usually think of Electromagnetic waves) which can radiate, and electromagnetic waves only self-propel themselves if the Electric & Magnetic fields are Sines or Cosines (since the relations between electric & magnetic fields are time derivatives; a sine creates a cosine and vice-versa).

So I think the "photons" will still be described as sinusoids. However, the antenna will probably output many different frequencies of photons (EM-waves), so the sawtooth wave will look like it's been decomposed into however many sinusoidal EM-waves by the antenna. Any photon that couldn't be described as a self-propagating sinusoidal wave would instead be "evanescent" - it will die out quickly, eg. a decaying exponential.

Whether the "photon" is really a sawtooth shape, or is really a superposition of many sinusoids, is sort of due to how we define photons and electromagnetic waves - presumably you could describe the same situation without only sinusoidal electromagnetic "photons" (or photon-packets as it were), but that's how all the math I've ever seen does it.

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  • $\begingroup$ The modes of an antenna are not photons and photons are not described by periodic functions. It doesn't even make sense to talk about photons, unless you are talking in a quantum field picture, which most certainly is not useful for macroscopic antennas. You have certainly never seen math that describes photons as sinusoids, at least not in a textbook worth keeping. $\endgroup$
    – CuriousOne
    Jun 29, 2016 at 20:37
  • $\begingroup$ You are free to make your answer factually correct and I will remove my down vote. $\endgroup$
    – CuriousOne
    Jun 29, 2016 at 20:41
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    $\begingroup$ Antennas are always described using waves, but the OP is asking about photons - conceptually these two are related, since with lasers, for example, you use both descriptions simultaneously. So I'm thinking the "photon" here would be some quanta of energy in the wave, the minimum that could be absorbed by another antenna. $\endgroup$
    – Demis
    Jun 29, 2016 at 20:42
  • $\begingroup$ I'm more interested in helping this guy understand rather than the number of arrow clicks I get. If you have something useful to add feel free to improve the answer yourself. $\endgroup$
    – Demis
    Jun 29, 2016 at 20:43
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    $\begingroup$ That the OP doesn't, yet, understand that photons are quantum field measurements and not classical or semi-classical objects is no excuse for a false answer. Nothing stops you from talking about photons correctly. If you look at correct quantum descriptions of lasers, then you will find the language of quantum field theory all over the place (i.e. creation and annihilation operators). Using those doesn't really make much sense for antennas, unless you are also throwing a density matrix in, which really won't return much beyond classical Maxwell. $\endgroup$
    – CuriousOne
    Jun 29, 2016 at 20:45

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